Computer graphics technology creates images from digital data-bases composed of mathematically-described models. Models may be defined in two dimensions or in three dimensions. A graphics system creates an image of a three-dimensional model to appear as it would if the model were real and viewed from a particular point in space. Such techniques have found broad utility in creating images for science, entertainment and advertising; for interactive computer aided design; and for many other applications.
The final two-dimensional image is ultimately displayed, for example, on a raster device such as a computer screen, laser printer or typographic device. The image is composed of an array of picture elements (pixels), which are the smallest units or "dots" on a raster display for which a color or gray shade may be set. The quality of the image depends upon the size and number of pixels. Larger quantities of smaller pixels yield higher resolution images.
Rendering entails calculating the color values or grayscale shade for each pixel to generate the desired image. The color or grayscale shade of each pixel depends, in turn, upon the lighting of the model, surface geometry, surface properties (i.e., the way a surface is assumed to reflect or absorb light) and the eyepoint position.
Traditional methods of rendering are described by Foley, et al., Computer Graphics: Principles and Practice, 2nd ed., Addison Wesley Publishing Company, 1990, ISBN 0-201-12110-7. The subject of calculation of lighting effects on surfaces is covered in detail by Roy Hall, Illumination and Color in Computer Generated Imagery, Springer-Verlag, 1988, ISBN 0-387-96774-5 which is herein incorporated by reference.
In what is called resolution-dependent rendering, models are converted to raster images in a continuous process that produces an image of a predetermined resolution based on the resolution of the output device. For resolution-independent rendering, an intermediate description of the model is first produced. This intermediate description is independent of the resolution of the output device and can be edited at one resolution and printed or otherwise output at another, typically much higher, resolution.
Traditional three-dimensional rendering methods are polygon-based. That is, models that are not directly formed of polygons are converted into polygons for rendering. Thus, for example, each curved surface is converted into an approximation of the surface made of small polygonal facets, usually triangles.
Traditional three-dimensional rendering methods are also resolution-dependent. Thus, the resolution of the output image is determined before the image is generated, and once generated the resolution generally cannot be increased even when displayed on a higher resolution device. Pixels in a rendered image may be replicated or interpolated to increase the total number of pixels, but extra pixels added by replication or interpolation do not increase the sharpness of the image. Therefore, the resolution of the image is not increased (even though its appearance can be made more pleasing to the eye) when displayed on a higher resolution device.
Resolution-dependent rendering methods have a number of disadvantages. One disadvantage is that producing a high resolution end-product image requires relatively large amounts of computer storage and processing. For example, high quality printing may require 2400 pixels per inch or more. At 2400 pixels per inch, an 8.times.10 inch image has over 460 million pixels, with one or more bytes of storage required for each pixel. That amount of storage is expensive and the processing to obtain it inconveniently slow.
Another disadvantage of resolution-dependent imagery is that the flexibility of editing is limited. For example, if a rendered model is moved slightly within the image by editing the pixels of the rendered version of the model, the uncovered portion of the image cannot be regenerated quickly because, in practice, the whole image is usually regenerated from scratch with the model moved in the database. The inefficiency of editing resolution-dependent images often forces the user to settle for lower resolution outputs than a particular output device is capable of generating because obtaining a higher resolution output would be too slow.
Unlike three-dimensional graphics rendering, two-dimensional rendering has been widely available in forms that work directly with curves and in forms that are resolution-independent. For example, products like Adobe Illustrator permit drawings to be made and edited in a resolution-independent format. This is helpful for the preparation of illustrations which are originated and edited on comparatively low-resolution (typically 72 pixels per inch) computer screens, but ultimately output on laser printers (300 to 600 pixels per inch) or typographic equipment (typically 1200 to 2400 pixels) per inch. The ability to edit in a lower resolution version saves equipment costs and computation time.
Another problem with resolution-dependent three-dimensional model renderings is the difficulty of combining those rendered images with resolution-independent, two-dimensional illustrations. Illustrators would benefit from combining both three-dimensional models and two-dimensional models in a resolution-independent format, and from being able to edit the combined illustration with a single tool set. For example, an illustration of a bottle with a label could be done by drawing the label in two-dimensions, rendering the bottle in three-dimensions, curving the label in three-dimensions to conform to the bottle shape, and positioning the label, bottle and perhaps other elements in a two-dimensional layout for printing. This type of application is difficult without a resolution-independent three-dimensional rendering method.
Resolution-independent rendering is more challenging for curved surfaces than for polygons. Moreover, surfaces having only one direction of curvature, such as a cylinder, are easier to render than surfaces having compound curvature, such as a bottleneck. Compound curves commonly have been rendered by first converting the modeled surface to an approximation made by triangles, which is time consuming and limited in accuracy. Work also has been done with direct resolution-dependent rendering of compound curves, for example, that of S. Chang, et al., "Rendering Cubic Curves and Surfaces with Integer Adaptive Forward Differencing," Computer Graphics, Vol. 23, No. 3, July 1989.
Objects of this invention are: (1) to provide a method for three-dimensional rendering that provides a resolution-independent, two-dimensional output; (2) to provide an improved method for three-dimensional rendering that will work with curved surfaces, including compound curved surfaces, without approximating these surfaces by triangles; and (3) to provide a three-dimensional rendering method that is compatible with existing two-dimensional computer illustration programs and with existing printing equipment so that adding three-dimensional models to illustrations is facilitated.